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1. If a1 = λ1i + µ1j + ν1k, a2 = λ2i + µ2j + ν2k, a3 = λ3i + µ3j + ν3k, where {i,j, k} is a standard basis, show
that
(a)
a1 · (a2 × a3) =
λ1 µ1 ν1
λ2 µ2 ν2
λ3 µ3 ν3
.
(b) Deduce that a2 · (a3 × a1), due to cyclic rotation of the vectors in a triple scalar product leaves the
value of the product unchanged.
(c) If r(t) = (3t
2 − 4)i + t
3
j + (t + 3)k, where {i,j, k} is a constant standard basis, find r˙ and ¨r. Deduce
the time derivative of r × r˙.
that
(a)
a1 · (a2 × a3) =
λ1 µ1 ν1
λ2 µ2 ν2
λ3 µ3 ν3
.
(b) Deduce that a2 · (a3 × a1), due to cyclic rotation of the vectors in a triple scalar product leaves the
value of the product unchanged.
(c) If r(t) = (3t
2 − 4)i + t
3
j + (t + 3)k, where {i,j, k} is a constant standard basis, find r˙ and ¨r. Deduce
the time derivative of r × r˙.
The sales of a company from 1993-1998 are given below:
Year 1993 1994 1995 1996 1997 1998
Sales (in lakhs of rupees) 40 45 50 55 60 65
Fit a linear curve using the least squares method. Hence find out the company’s sales in 1999.
Year 1993 1994 1995 1996 1997 1998
Sales (in lakhs of rupees) 40 45 50 55 60 65
Fit a linear curve using the least squares method. Hence find out the company’s sales in 1999.
Can you Solve this? :)
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A skateboarder rolls horizontally off the top of a staircase at a speed of 18 ms-1 and at the bottom of the stairs which has a horizontal length of 9 m as
.
Calculate the skater's vertical displacement during the jump
.
Calculate the skater's vertical displacement during the jump
Microsoft SQL server is a relational database server developed by Microsoft : It is a software product whose primary function is to store and retrieve data as requested by other software application be it those on the same computer or those running on another computer across a network (including the internet ). Compare MS SQL with other database and state the advantages of MS SQL over other database?
Find the working application with Derivation and upload the same here. With the same application answer the bellowed mentioned question.
1) How does the above application is working with derivation.
2) Which derivative method is used in the same
3) Can we used any other method in the same application. If yes which and if no why?
1) How does the above application is working with derivation.
2) Which derivative method is used in the same
3) Can we used any other method in the same application. If yes which and if no why?
what are the elements of short story writing ? explain briefly and also express your views on the given topic in paragraph form. it should be comprise of 100-130 words "young generation is more caution about their physical appearance".
you are student of business administration at the end of section you are required to do one year internship experience in a well reputed software company (Adam soft) write a letter of enquiry to director of software company (Adam soft) about internship opportunities and present yourself fully enthusiastic. motivated and active participant.
I was curious about how this will work if something many feet like let's say 100ft tall how will you do the weight of it? Like if you 100ft tall or 300ft it doesn't matter how can weight be determined of the height.
compute the value of 410-78 using 8-bit sign magnitude in binary
